Complex numbers are numbers that consist of a real part and an imaginary part. They are expressed in the form a + bi , where a is the real part, b is the imaginary part, and i is the imaginary unit, defined as the square root of -1. Complex numbers can be used to solve equations that do not have real solutions, such as x^2 + 1 = 0 . These numbers can be represented graphically on the complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part. Complex numbers have various applications in fields like engineering, physics, and computer science, particularly in signal processing and control theory.